This work uses a combination of a variational auto-encoder and generative adversarial network to compare different dark energy models in light of observations, e.g., the distance modulus from type Ia supernovae. The network finds an analytical variational approximation to the true posterior of the latent parameters in the models, yielding consistent model comparison results with those derived by the standard Bayesian method, which suffers from a computationally expensive integral over the parameters in the product of the likelihood and the prior. The parallel computational nature of the network together with the stochastic gradient descent optimization technique leads to an efficient way to compare the physical models given a set of observations. The converged network also provides interpolation for a dataset, which is useful for data reconstruction.
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